From the sum ${2 y}^{2} + 3 y z, - y^{2} y z - z^{2}$ and $y z + {2 z}^{2}$ subtract the sum $3 y^{2} + z^{2}$ and $y^{2} + y z + z^{2} .$

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Solution

Sum of $2 y^{2} + 3 y z, - y^{2} - y z - z^{2}$ and $y z - 2 z^{2}$
$= 2 y^{2} + 3 y z - y^{2} - y z - z^{2} + y z + 2 z^{2}$
$= y^{2} + z^{2} + 3 y z$

And sum $= 3 y^{2} - z^{2}, (- y^{2} + y z + z^{2})$
$= 3 y^{2} - z^{2} - y^{2} + y z + z^{2}$
$= 2 y^{2} + y z$

We need to find:
$(y^{2} + z^{2} + 3 y z) - (2 y^{2} + y z)$
$= y^{2} + z^{2} + 3 y z - 2 y^{2} - y z$
$= - y^{2} + z^{2} + 2 y z$
$= - y^{2} + 2 y z + z^{2}$

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